Why are we able to show structures of compounds with different position of electron, but with same position of them? Shouldn't the structure become unstable due to this?

Let's take benzene for the example of resonance.We know that in reality benzene has no pure single or double bond. How can this be possible?

The bond length for $\ce{C-C}$ and $\ce{C=C}$ bonds in benzene is same which is $1.39~\mathring{\mathrm{A}}$. This is due to partial single and double bond between carbon atom, which is due to resonance. Why is there a resonance? Why can't benzene be happy with three alternate single and double bond between each carbon atom?

However, I decided to somewhat clarify the matter emphasising few important points. And I will start by quoting the OP.

We know that in reality benzene has no pure single or double bond.

Now please, take a deep breathe and repeat with me: there are no bonds. In reality we do have electrons and nuclei that constitutes a molecule, but a chemical bond is merely a theoretical concept introduced in the framework of a scientific theory. In other words, chemical bonds do not exist in the same sense as electrons and nuclei do.

For instance, the concept of resonance was introduced by Linus Pauling in the framework of the so-called valence bond theory, according to which

a covalent bond is formed between the two atoms by the overlap of half
filled valence atomic orbitals of each atom containing one unpaired
electron.

So, this is the way the concept of chemical bonding enters the scene in the valence bond theory: a chemical bond is used to describe overlapped atomic orbitals of two atoms in a molecule. Note that atomic orbitals also do not exist in the same sense as electrons and nuclei do, but an orbital has at least some strict mathematical and physical meaning, while a chemical bond, as introduced above, does not. Read the above quote carefully one more time: it is not even a definition! What we just say is that whenever half filled valence atomic orbitals of two atoms overlap a covalent bond is formed, but we do not say what exactly is a covalent bond. It is just something; something which is formed whenever orbitals overlap. It is a concept, purely theoretical construction. It is practically helpful in description of a reality, but no one will say that it is actually a part of it.

Do not be afraid of all this business, because it is the way science generally works. Scientific theories basically tell us how nature could be described, and they do so in the language of mathematics, since it is the only language nature can unambiguously "speak" with us. However, it is often so tempting to force it to speak with us in a different language, in a language of our theoretical concepts (such as, for instance, the concept of a chemical bonding), no matter how fuzzy they are. This is a very dangerous road, because, after all, who are we to tell nature which language to speak? Nature will likely refuse to "speak" with us in that language, and that would be it.

That is what actually happened with the valence bond theory as it was originally formulated. Indeed, all carbon-carbon bond lengths are equal in benzene, but the valence bond theory were not able to account for that simple fact. Nature refused to "speak" with us in the language of chemical bonding. At that point chemists had two choices: either abandon the valence bond theory or introduce another theoretical concept into it, introduce a new word in our language making it possible to communicate with nature in this language. The concept of a chemical bonding was already so tremendously useful in chemistry that the choice was actually predetermined, and in 1928 Linus Pauling introduced the concept of resonance between several valence-bond structures of a molecule.

What is resonance? Is it a physical process? No way! It is just a concept, a word, used to describe

delocalized electrons within certain molecules or polyatomic ions
where the bonding cannot be expressed by a single Lewis formula.

The word "resonance" was probably not the best choice by Pauling, since it gives an unwanted feeling that the molecule actually do oscillate back and forth between the structures, which is, as I said, not the case. But putting aside its somewhat misleading name, the concept of resonance is as good as the concept of chemical bonding and many other concepts in chemistry and other sciences.

Delocalization is characteristic of the molecular orbital theory
concerning the structure of atoms. Rather than the lone pair of
electrons contained in specific bonds (as in the valence-bond theory),
the MO (molecular-orbital theory) theorizes that electrons exist in
orbitals that are spread over the entire molecule. The MO theory
explains molecules such as ozone and benzene, which cannot be drawn
satisfactorily with one Lewis structure, and are therefore described
as resonance hybrids. Molecular orbitals solve this issue through the
concept of delocalized electrons.

When orbitals overlap, many of the orbitals are in hybrid states. Like
delocalization, hybridization occurs to promote symmetry and
stability. Delocalized electrons are often found in covalently bonded
molecules that alternate single and multiple (usually double) bonds.
Also, they frequently occur in aromatic systems and in mesoionic
systems which means that they cannot exist in merely one resonance
structure (they can and do exist in many resonance structures).

Delocalization matters for several reasons. One, spreading electron
densities over a great area creates greater stability for the
molecule. Spreading electrons creates charge distribution.
Therefore, chemical reactions expected because of a hypothesized
configuration may not occur, a stable product is formed more readily
in a reaction. Delocalization of electrons also paves the way for
conductivity while in spectroscopy, wavelenght absorbtion is also
based on resonance stability and delocalization of electrons.

$\begingroup$Thank you for adding the source. Rather than quoting the entire passage, which is already available online, it's best to illuminate what is written with your own prose.$\endgroup$
– jonsca♦Feb 4 '15 at 0:13

A chemical becomes reactive when it has either excess or insufficient electron cloud. For example, in case of Ammonia $\ce {NH}_3$, Nitrogen has a lone pair of electron. Thus, it has excess of electron cloud. It can donate these electrons. Hence, Ammonia is reactive. Similarly, Aluminium is highly electropositive and has empty p-orbital. Hence, it can accept electrons and is also reactive.

In case of Benzene, the electrons are delocalised, that is, the electron cloud is spread over the entire ring of Benzene. Thus, there is no accumulation of charge in the ring at one place. This gives extra stability to Benzene. And every molecule wants to attain maximum stability.

If resonance didn't exist in Benzene, then it would react easily with many reagents. Since each of the carbons is $\ce {sp}^2$ hybridised, that is, each carbon is quite electronegative, and has the capacity to react.

Maybe there is a better answer to your question. This is what I can think as the reason.